Problem related to Coloumb's force

[gracy]

Homework Statement

One more query.Two identical small bodies each of mass m and charge q are suspended from two strings each of length l from a fixed point.This whole system is taken into an orbiting artificial satellite, then find the tension in the two strings?

Homework Equations

The Attempt at a Solution

I know in satellite g=0. Therefore there won't be any weight acting downwards
only forces which exists between the balls will be
Coulombs force of repulsion + mutual gravitational force attraction between bodies + gravitational force of attraction of the satellite on the bodies

However, magnitude of above said gravitational forces will be negligible as compared to coulombs force. Hence this coulombs force of repulsion can be considered the only force between the balls which will repel them .But the answer given is T= (1/4πε0)*q^2/4l^2
This suggests r=2l
I want to know how to find "r"how r came out to be 2l?
probably the following image will suit the situation in the question.

 

[Orodruin]

I want to know how to find "r"how r came out to be 2l?

In your image, what will the angle $\theta$ be in the absence of an external gravitational field?

 

[gracy]

what will the angle θ\theta be in the absence of an external gravitational field?

No.idea.help me out.Give me a hint.

 

[Orodruin]

What forces are acting on the masses? What will be the requirement for the masses being in equilibrium?

 

[gracy]

What forces are acting on the masses? What will be the requirement for the masses being in equilibrium?

I think i have put all that I know.

I know in satellite g=0. Therefore there won't be any weight acting downwards
only forces which exists between the balls will be
Coulombs force of repulsion + mutual gravitational force attraction between bodies + gravitational force of attraction of the satellite on the bodies

However, magnitude of above said gravitational forces will be negligible as compared to coulombs force. Hence this coulombs force of repulsion can be considered the only force between the balls which will repel them

 

[Orodruin]

Hence this coulombs force of repulsion can be considered the only force between the balls which will repel them .

So if this is the only force, how will the masses end up in relation to each other? What is the only possible equilibrium position?

 

[gracy]

this coulombs force of repulsion can be considered the only force between the balls which will repel them

is it wrong?

 

[Orodruin]

is it wrong?

There is also the tension from the strings. You need to consider that the masses should be in equilibrium.

 

[gracy]

There is also the tension from the strings.

Yes it is.I meant only force to balance tension.

force of repulsion can be considered the only force between the balls which will repel them

 

[Orodruin]

Yes it is.I meant only force to balance tension.

So in which direction is the tension?

 

[gracy]

in which direction is the tension?

opposite to repulsive coulomb force.

 

[Orodruin]

opposite to repulsive coulomb force.

Which means that the configuration must look how?

 

[gracy]

Which means that the configuration must look how?

as if bodies were attracting each other

 

[DrClaude]

Lets do a thought experiment. Imagine that the two charges are held exactly where they are in the picture in the OP. You then let go of the charges. What happens?

 

[Doc Al]

as if bodies were attracting each other

This is a bit unclear.

Do this: Name the forces that act on each mass. Hint: Only two (significant) forces act.

Draw (or describe) the configuration of the masses. What angle will the strings make?

 

[gracy]

Imagine that the two charges are held exactly where they are in the picture in the OP. You then let go of the charges. What happens?

I think theta will start increasing because of repulsion.

 

[gracy]

Name the forces that act on each mass

Tension and repulsion.

 

[DrClaude]

I think theta will start increasing because of repulsion.

Does it increase forever, or does it stop at one point?

 

[gracy]

I don't know whether it is correct but i think tension force will be able to be split into one horizontal force and one vertical.The horizontal one would cancel the repulsive force.But one problem with this is then vertical force would be unbalanced so net force would be vertical so motion should be in vertical direction.

Does it increase forever, or does it stop at one point?

They would stop when The horizontal component of tension would cancel the repulsive force.

 

[Doc Al]

Tension and repulsion.

Good. The tension force from the string and the Coulomb electrostatic force.

 

[Orodruin]

They would stop when The horizontal component of tension would cancel the repulsive force.

So how does the setup look then?

 

[gracy]

So how does the setup look then?

Am I supposed to draw the situation.

 

[Orodruin]

Am I supposed to draw the situation.

Try to describe it, what is the angle theta in your figure going to be?

 

[gracy]

probably the following image will suit the situation in the question.

One thing i would like to clarify is the above picture was not a part of the question in op.I copied it from google images.So as we can see nothing bout theta is mentioned in the question.

 

[Orodruin]

One thing i would like to clarify is the above picture was not a part of the question in op.I copied it from google images.So as we can see nothing bout theta is mentioned in the question.

I know that, but I am asking you what it will be anyway. It is fundamental for the understanding of the problem.

 

[DrClaude]

One thing i would like to clarify is the above picture was not a part of the question in op.I copied it from google images.So as we can see nothing bout theta is mentioned in the question.

It doesn't matter, that picture is very useful in anyway.

What I'm trying to do (and, I believe, so is Orodruin) is to get you to visualize what is happening. Once you have a good mental picture, the rest will be simple.

 

[gracy]

So how does the setup look then?

l (lower case L)cos theta =kq^2/d^2
here d=distance between the bodies when horizontal component of tension cancels the repulsive force.And k is coulomb constant having value of 9 multiplied by 10^9.

 

[Doc Al]

Imagine two like charges (they repel) connected by a string in outer space (no gravity). What happens?

 

[gracy]

They will repel and the string will break if the repulsive force is greater than the tension in the string.

 

[Doc Al]

They will repel and the string will break if the repulsive force is greater than the tension in the string.

Good. Assuming the string is strong enough, what will the final (equilibrium) position look like?

 

[gracy]

It will be same as initial position.

 

[DrClaude]

I think theta will start increasing because of repulsion.

It will be same as initial position.

You are contradicting yourself.

 

[Doc Al]

It will be same as initial position.

Really? That depends on the initial position, doesn't it?

Try this. The string is 3 meters long. Start out with the charges 1 meter apart. When equilibrium is reached, how far apart are the charges?

 

[gracy]

When equilibrium is reached, how far apart are the charges?

it depends on when tension force balances with coloumbs force .

 

[gracy]

Really? That depends on the initial position, doesn't it?

I thought charges were at the ends of string.